Chapter 4 – 9
Algebra 2
Rational Expressions
Inverse Variation
Inverse Variation –
The table shows the time needed to bike 24 miles pedaling at different rates.
Rate (mi/h) Time (h)
3
8
6
4
12
2
24
1
Draw a graph to show the relationship between rate and time.
Write the equation of the graph.
How many hours would it take to bike the 24 miles if the rate was 4 mph?
Examples
1) Graph the following
a) xy = 12
b) xy = -8
2) Suppose that x and y vary inversely, and x = 3 when y = -5. Write the function that models inverse
variation, and then find y when x = 7.
3) Suppose that x and y vary inversely, and x = 0.3 when y = 1.4. Write the function that models inverse
variation, and then find x when y = 10.
4) In the table, y varies inversely as x. What is the value of m?
x
2
4
m
y
18
9
3
5) If x varies inversely as y, and x = 9 when y = 8, find x when y = 12.
6) The diameter of a wheel varies inversely as the number of revolutions that the wheel makes to cover a
certain distance. If a wheel with a 26-inch diameter makes 10 revolutions in covering a certain distance,
how many revolutions will a wheel with a diameter of 20 inches make in covering the same distance?
7) According to Boyle’s Law, the pressure of a compressed gas is inversely proportional to the volume.
If the pressure is 25 pounds per square inch when the volume of gas is 400 cubic inches, the pressure
when the gas is compressed to 200 cubic inches is how many pounds per square inch?
8) Every year a band is paid $350 to play at the county fair. Let a represent the amount each member
receives, and let n represent the number of members in the band. Write the inverse variation
relationship between a and n.
Then find out how much each member will earn if the band has 5 members.
9) When air is pumped into an automobile tire, the pressure is inversely proportional to the volume. If
the pressure if 35 pounds when the volume is 120 cubic inches, what is the pressure, in pounds, when
the volume is 140 cubic inches?
10) Which graph represents an inverse variation between stream velocity and the distance from
the center of the stream?